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A Eulerian—Lagrangian model has been developed to simulate particle attachment to surfaces with arc-shaped ribs in a two-dimensional channel flow at low Reynolds numbers. Numerical simulation has been performed to improve the quantitative understanding of how rib geometries enhance shear rates and particle-surface interact for various particle sizes and flow velocities. The enhanced shear rate is attributed to the wavy flows that develop over the ribbed surface and the weak vortices that form between adjacent ribs. Varying pitch-to-height ratio can alter the amplitude of the wavy flow and the angle of attack of the fluid on the ribs. In the presence of these two competing factors, the rib geometry with a pitch-to-height ratio of two demonstrates the greatest shear rate and the lowest fraction of particle attachment. However, the ribbed surfaces have negligible effects on small particles at low velocities. A force analysis identifies a threshold shear rate to reduce particle attachment. The simulated particle distributions over the ribbed surfaces are highly non-uniform for larger particles at higher velocities. The understanding of the effect of surface topography on particle attachment will benefit the design of surface textures for mitigating particulate fouling in a wide range of applications.